// SPDX-License-Identifier: GPL-2.0-or-later
/*
  Red Black Trees
  (C) 1999  Andrea Arcangeli <andrea@suse.de>
  (C) 2002  David Woodhouse <dwmw2@infradead.org>
  (C) 2012  Michel Lespinasse <walken@google.com>


  linux/lib/rbtree.c
*/

#include <rbtree_augmented.h> // #include <linux/rbtree_augmented.h>
//#include <linux/export.h>

/*
 * red-black trees properties:  https://en.wikipedia.org/wiki/Rbtree
 *
 *  1) A node is either red or black
 *  2) The root is black
 *  3) All leaves (NULL) are black
 *  4) Both children of every red node are black
 *  5) Every simple path from root to leaves contains the same number
 *     of black nodes.
 *
 *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
 *  consecutive red nodes in a path and every red node is therefore followed by
 *  a black. So if B is the number of black nodes on every simple path (as per
 *  5), then the longest possible path due to 4 is 2B.
 *
 *  We shall indicate color with case, where black nodes are uppercase and red
 *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
 *  parentheses and have some accompanying text comment.
 */

/*
 * Notes on lockless lookups:
 *
 * All stores to the tree structure (rb_left and rb_right) must be done using
 * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
 * tree structure as seen in program order.
 *
 * These two requirements will allow lockless iteration of the tree -- not
 * correct iteration mind you, tree rotations are not atomic so a lookup might
 * miss entire subtrees.
 *
 * But they do guarantee that any such traversal will only see valid elements
 * and that it will indeed complete -- does not get stuck in a loop.
 *
 * It also guarantees that if the lookup returns an element it is the 'correct'
 * one. But not returning an element does _NOT_ mean it's not present.
 *
 * NOTE:
 *
 * Stores to __rb_parent_color are not important for simple lookups so those
 * are left undone as of now. Nor did I check for loops involving parent
 * pointers.
 */

static inline void rb_set_black(struct rb_node *rb)
{
    rb->__rb_parent_color += RB_BLACK;
}

static inline struct rb_node *rb_red_parent(struct rb_node *red)
{
    return (struct rb_node *)red->__rb_parent_color;
}

/*
 * Helper function for rotations:
 * - old's parent and color get assigned to new
 * - old gets assigned new as a parent and 'color' as a color.
 */
static inline void
__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
                        struct rb_root *root, int color)
{
    struct rb_node *parent = rb_parent(old);
    new->__rb_parent_color = old->__rb_parent_color;
    rb_set_parent_color(old, new, color);
    __rb_change_child(old, new, parent, root);
}
static inline void
__rb_insert(struct rb_node *node, struct rb_root *root,
            void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
    struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;

    while (true) {
        /*
         * Loop invariant: node is red.
         */
        //if (unlikely(!parent)) {
        if (parent == NULL) { // if (!parent) {
            /*
             * The inserted node is root. Either this is the
             * first node, or we recursed at Case 1 below and
             * are no longer violating 4).
             */
            rb_set_parent_color(node, NULL, RB_BLACK);
            break;
        }

        /*
         * If there is a black parent, we are done.
         * Otherwise, take some corrective action as,
         * per 4), we don't want a red root or two
         * consecutive red nodes.
         */
        if(rb_is_black(parent))
            break;

        gparent = rb_red_parent(parent);

        tmp = gparent->rb_right;
        if (parent != tmp) {	/* parent == gparent->rb_left */
            if (tmp && rb_is_red(tmp)) {
                /*
                 * Case 1 - node's uncle is red (color flips).
                 *
                 *       G            g
                 *      / \          / \
                 *     p   u  -->   P   U
                 *    /            /
                 *   n            n
                 *
                 * However, since g's parent might be red, and
                 * 4) does not allow this, we need to recurse
                 * at g.
                 */
                rb_set_parent_color(tmp, gparent, RB_BLACK);
                rb_set_parent_color(parent, gparent, RB_BLACK);
                node = gparent;
                parent = rb_parent(node);
                rb_set_parent_color(node, parent, RB_RED);
                continue;
            }

            tmp = parent->rb_right;
            if (node == tmp) {
                /*
                 * Case 2 - node's uncle is black and node is
                 * the parent's right child (left rotate at parent).
                 *
                 *      G             G
                 *     / \           / \
                 *    p   U  -->    n   U
                 *     \           /
                 *      n         p
                 *
                 * This still leaves us in violation of 4), the
                 * continuation into Case 3 will fix that.
                 */
                tmp = node->rb_left;
                parent->rb_right = tmp;// WRITE_ONCE(parent->rb_right, tmp);
                node->rb_left = parent; // WRITE_ONCE(node->rb_left, parent);
                if (tmp)
                    rb_set_parent_color(tmp, parent,
                                        RB_BLACK);
                rb_set_parent_color(parent, node, RB_RED);
                augment_rotate(parent, node);
                parent = node;
                tmp = node->rb_right;
            }

            /*
             * Case 3 - node's uncle is black and node is
             * the parent's left child (right rotate at gparent).
             *
             *        G           P
             *       / \         / \
             *      p   U  -->  n   g
             *     /                 \
             *    n                   U
             */
            gparent->rb_left = tmp;// WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
            parent->rb_right = gparent;// WRITE_ONCE(parent->rb_right, gparent);
            if (tmp)
                rb_set_parent_color(tmp, gparent, RB_BLACK);
            __rb_rotate_set_parents(gparent, parent, root, RB_RED);
            augment_rotate(gparent, parent);
            break;
        } else {
            tmp = gparent->rb_left;
            if (tmp && rb_is_red(tmp)) {
                /* Case 1 - color flips */
                rb_set_parent_color(tmp, gparent, RB_BLACK);
                rb_set_parent_color(parent, gparent, RB_BLACK);
                node = gparent;
                parent = rb_parent(node);
                rb_set_parent_color(node, parent, RB_RED);
                continue;
            }

            tmp = parent->rb_left;
            if (node == tmp) {
                /* Case 2 - right rotate at parent */
                tmp = node->rb_right;
                parent->rb_left = tmp;// WRITE_ONCE(parent->rb_left, tmp);
                node->rb_right = parent;// WRITE_ONCE(node->rb_right, parent);
                if (tmp)
                    rb_set_parent_color(tmp, parent,
                                        RB_BLACK);
                rb_set_parent_color(parent, node, RB_RED);
                augment_rotate(parent, node);
                parent = node;
                tmp = node->rb_left;
            }

            /* Case 3 - left rotate at gparent */
            gparent->rb_right = tmp;// WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
            parent->rb_left = gparent;// WRITE_ONCE(parent->rb_left, gparent);
            if (tmp)
                rb_set_parent_color(tmp, gparent, RB_BLACK);
            __rb_rotate_set_parents(gparent, parent, root, RB_RED);
            augment_rotate(gparent, parent);
            break;
        }
    }
}

/*
 * Inline version for rb_erase() use - we want to be able to inline
 * and eliminate the dummy_rotate callback there
 */
static inline void
____rb_erase_color(struct rb_node *parent, struct rb_root *root,
                   void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
    struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;

    while (true) {
        /*
         * Loop invariants:
         * - node is black (or NULL on first iteration)
         * - node is not the root (parent is not NULL)
         * - All leaf paths going through parent and node have a
         *   black node count that is 1 lower than other leaf paths.
         */
        sibling = parent->rb_right;
        if (node != sibling) {	/* node == parent->rb_left */
            if (rb_is_red(sibling)) {
                /*
                 * Case 1 - left rotate at parent
                 *
                 *     P               S
                 *    / \             / \
                 *   N   s    -->    p   Sr
                 *      / \         / \
                 *     Sl  Sr      N   Sl
                 */
                tmp1 = sibling->rb_left;
                parent->rb_right = tmp1;// WRITE_ONCE(parent->rb_right, tmp1);
                sibling->rb_left = parent;// WRITE_ONCE(sibling->rb_left, parent);
                rb_set_parent_color(tmp1, parent, RB_BLACK);
                __rb_rotate_set_parents(parent, sibling, root,
                                        RB_RED);
                augment_rotate(parent, sibling);
                sibling = tmp1;
            }
            tmp1 = sibling->rb_right;
            if (tmp1 == NULL || rb_is_black(tmp1)) { // if (!tmp1 || rb_is_black(tmp1)) {
                tmp2 = sibling->rb_left;
                if (tmp2 == NULL || rb_is_black(tmp2)) { // if (!tmp2 || rb_is_black(tmp2)) {
                    /*
                     * Case 2 - sibling color flip
                     * (p could be either color here)
                     *
                     *    (p)           (p)
                     *    / \           / \
                     *   N   S    -->  N   s
                     *      / \           / \
                     *     Sl  Sr        Sl  Sr
                     *
                     * This leaves us violating 5) which
                     * can be fixed by flipping p to black
                     * if it was red, or by recursing at p.
                     * p is red when coming from Case 1.
                     */
                    rb_set_parent_color(sibling, parent,
                                        RB_RED);
                    if (rb_is_red(parent))
                        rb_set_black(parent);
                    else {
                        node = parent;
                        parent = rb_parent(node);
                        if (parent)
                            continue;
                    }
                    break;
                }
                /*
                 * Case 3 - right rotate at sibling
                 * (p could be either color here)
                 *
                 *   (p)           (p)
                 *   / \           / \
                 *  N   S    -->  N   sl
                 *     / \             \
                 *    sl  Sr            S
                 *                       \
                 *                        Sr
                 *
                 * Note: p might be red, and then both
                 * p and sl are red after rotation(which
                 * breaks property 4). This is fixed in
                 * Case 4 (in __rb_rotate_set_parents()
                 *         which set sl the color of p
                 *         and set p RB_BLACK)
                 *
                 *   (p)            (sl)
                 *   / \            /  \
                 *  N   sl   -->   P    S
                 *       \        /      \
                 *        S      N        Sr
                 *         \
                 *          Sr
                 */
                tmp1 = tmp2->rb_right;
                sibling->rb_left = tmp1;// WRITE_ONCE(sibling->rb_left, tmp1);
                tmp2->rb_right = sibling;// WRITE_ONCE(tmp2->rb_right, sibling);
                parent->rb_right = tmp2;// WRITE_ONCE(parent->rb_right, tmp2);
                if (tmp1)
                    rb_set_parent_color(tmp1, sibling,
                                        RB_BLACK);
                augment_rotate(sibling, tmp2);
                tmp1 = sibling;
                sibling = tmp2;
            }
            /*
             * Case 4 - left rotate at parent + color flips
             * (p and sl could be either color here.
             *  After rotation, p becomes black, s acquires
             *  p's color, and sl keeps its color)
             *
             *      (p)             (s)
             *      / \             / \
             *     N   S     -->   P   Sr
             *        / \         / \
             *      (sl) sr      N  (sl)
             */
            tmp2 = sibling->rb_left;
            parent->rb_right = tmp2;// WRITE_ONCE(parent->rb_right, tmp2);
            sibling->rb_left = parent;// WRITE_ONCE(sibling->rb_left, parent);
            rb_set_parent_color(tmp1, sibling, RB_BLACK);
            if (tmp2)
                rb_set_parent(tmp2, parent);
            __rb_rotate_set_parents(parent, sibling, root,
                                    RB_BLACK);
            augment_rotate(parent, sibling);
            break;
        } else {
            sibling = parent->rb_left;
            if (rb_is_red(sibling)) {
                /* Case 1 - right rotate at parent */
                tmp1 = sibling->rb_right;
                parent->rb_left = tmp1;// WRITE_ONCE(parent->rb_left, tmp1);
                sibling->rb_right = parent;// WRITE_ONCE(sibling->rb_right, parent);
                rb_set_parent_color(tmp1, parent, RB_BLACK);
                __rb_rotate_set_parents(parent, sibling, root,
                                        RB_RED);
                augment_rotate(parent, sibling);
                sibling = tmp1;
            }
            tmp1 = sibling->rb_left;
            if (tmp1 == NULL || rb_is_black(tmp1)) { // if (!tmp1 || rb_is_black(tmp1)) {
                tmp2 = sibling->rb_right;
                if (tmp2 == NULL || rb_is_black(tmp2)) { // if (!tmp2 || rb_is_black(tmp2)) {
                    /* Case 2 - sibling color flip */
                    rb_set_parent_color(sibling, parent,
                                        RB_RED);
                    if (rb_is_red(parent))
                        rb_set_black(parent);
                    else {
                        node = parent;
                        parent = rb_parent(node);
                        if (parent)
                            continue;
                    }
                    break;
                }
                /* Case 3 - left rotate at sibling */
                tmp1 = tmp2->rb_left;
                sibling->rb_right = tmp1;// WRITE_ONCE(sibling->rb_right, tmp1);
                tmp2->rb_left = sibling;// WRITE_ONCE(tmp2->rb_left, sibling);
                parent->rb_left = tmp2;// WRITE_ONCE(parent->rb_left, tmp2);
                if (tmp1)
                    rb_set_parent_color(tmp1, sibling,
                                        RB_BLACK);
                augment_rotate(sibling, tmp2);
                tmp1 = sibling;
                sibling = tmp2;
            }
            /* Case 4 - right rotate at parent + color flips */
            tmp2 = sibling->rb_right;
            parent->rb_left = tmp2;// WRITE_ONCE(parent->rb_left, tmp2);
            sibling->rb_right = parent;// WRITE_ONCE(sibling->rb_right, parent);
            rb_set_parent_color(tmp1, sibling, RB_BLACK);
            if (tmp2)
                rb_set_parent(tmp2, parent);
            __rb_rotate_set_parents(parent, sibling, root,
                                    RB_BLACK);
            augment_rotate(parent, sibling);
            break;
        }
    }
}

/* Non-inline version for rb_erase_augmented() use */
void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
                      void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
    ____rb_erase_color(parent, root, augment_rotate);
}
// EXPORT_SYMBOL(__rb_erase_color);

/*
 * Non-augmented rbtree manipulation functions.
 *
 * We use dummy augmented callbacks here, and have the compiler optimize them
 * out of the rb_insert_color() and rb_erase() function definitions.
 */

static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}

static const struct rb_augment_callbacks dummy_callbacks = {
    .propagate = dummy_propagate,
    .copy = dummy_copy,
    .rotate = dummy_rotate
};

void rb_insert_color(struct rb_node *node, struct rb_root *root)
{
    __rb_insert(node, root, dummy_rotate);
}
// EXPORT_SYMBOL(rb_insert_color);

void rb_erase(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *rebalance;
    rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
    if (rebalance)
        ____rb_erase_color(rebalance, root, dummy_rotate);
}
// EXPORT_SYMBOL(rb_erase);

/*
 * Augmented rbtree manipulation functions.
 *
 * This instantiates the same __always_inline functions as in the non-augmented
 * case, but this time with user-defined callbacks.
 */

void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
                           void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
    __rb_insert(node, root, augment_rotate);
}
// EXPORT_SYMBOL(__rb_insert_augmented);

/*
 * This function returns the first node (in sort order) of the tree.
 */
struct rb_node *rb_first(const struct rb_root *root)
{
    struct rb_node	*n;

    n = root->rb_node;
    if (n == NULL) // if (!n)
        return NULL;
    while (n->rb_left)
        n = n->rb_left;
    return n;
}
// EXPORT_SYMBOL(rb_first);

struct rb_node *rb_last(const struct rb_root *root)
{
    struct rb_node	*n;

    n = root->rb_node;
    if (n == NULL) // if (!n)
        return NULL;
    while (n->rb_right)
        n = n->rb_right;
    return n;
}
// EXPORT_SYMBOL(rb_last);

struct rb_node *rb_next(const struct rb_node *node)
{
    struct rb_node *parent;

    if (RB_EMPTY_NODE(node))
        return NULL;

    /*
     * If we have a right-hand child, go down and then left as far
     * as we can.
     */
    if (node->rb_right) {
        node = node->rb_right;
        while (node->rb_left)
            node = node->rb_left;
        return (struct rb_node *)node;
    }

    /*
     * No right-hand children. Everything down and left is smaller than us,
     * so any 'next' node must be in the general direction of our parent.
     * Go up the tree; any time the ancestor is a right-hand child of its
     * parent, keep going up. First time it's a left-hand child of its
     * parent, said parent is our 'next' node.
     */
    while ((parent = rb_parent(node)) && node == parent->rb_right)
        node = parent;

    return parent;
}
// EXPORT_SYMBOL(rb_next);

struct rb_node *rb_prev(const struct rb_node *node)
{
    struct rb_node *parent;

    if (RB_EMPTY_NODE(node))
        return NULL;

    /*
     * If we have a left-hand child, go down and then right as far
     * as we can.
     */
    if (node->rb_left) {
        node = node->rb_left;
        while (node->rb_right)
            node = node->rb_right;
        return (struct rb_node *)node;
    }

    /*
     * No left-hand children. Go up till we find an ancestor which
     * is a right-hand child of its parent.
     */
    while ((parent = rb_parent(node)) && node == parent->rb_left)
        node = parent;

    return parent;
}
// EXPORT_SYMBOL(rb_prev);

void rb_replace_node(struct rb_node *victim, struct rb_node *new,
                     struct rb_root *root)
{
    struct rb_node *parent = rb_parent(victim);

    /* Copy the pointers/colour from the victim to the replacement */
    *new = *victim;

    /* Set the surrounding nodes to point to the replacement */
    if (victim->rb_left)
        rb_set_parent(victim->rb_left, new);
    if (victim->rb_right)
        rb_set_parent(victim->rb_right, new);
    __rb_change_child(victim, new, parent, root);
}
// EXPORT_SYMBOL(rb_replace_node);
/*
void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
			 struct rb_root *root)
{
	struct rb_node *parent = rb_parent(victim);

	// Copy the pointers/colour from the victim to the replacement
	*new = *victim;

	// Set the surrounding nodes to point to the replacement
	if (victim->rb_left)
		rb_set_parent(victim->rb_left, new);
	if (victim->rb_right)
		rb_set_parent(victim->rb_right, new);

	// Set the parent's pointer to the new node last after an RCU barrier
	// so that the pointers onwards are seen to be set correctly when doing
	// an RCU walk over the tree.

	__rb_change_child_rcu(victim, new, parent, root);
}
EXPORT_SYMBOL(rb_replace_node_rcu);
*/
static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
{
    for (;;) {
        if (node->rb_left)
            node = node->rb_left;
        else if (node->rb_right)
            node = node->rb_right;
        else
            return (struct rb_node *)node;
    }
}

struct rb_node *rb_next_postorder(const struct rb_node *node)
{
    const struct rb_node *parent;
    if (node == NULL) // if (!node)
        return NULL;
    parent = rb_parent(node);

    /* If we're sitting on node, we've already seen our children */
    if (parent && node == parent->rb_left && parent->rb_right) {
        /* If we are the parent's left node, go to the parent's right
         * node then all the way down to the left */
        return rb_left_deepest_node(parent->rb_right);
    } else
        /* Otherwise we are the parent's right node, and the parent
         * should be next */
        return (struct rb_node *)parent;
}
// EXPORT_SYMBOL(rb_next_postorder);

struct rb_node *rb_first_postorder(const struct rb_root *root)
{
    if (root->rb_node == NULL) // if (!root->rb_node)
        return NULL;

    return rb_left_deepest_node(root->rb_node);
}
// EXPORT_SYMBOL(rb_first_postorder);
